The (4, 0) AND (4, 4) SUPERSYMMETRIC NONLINEAR Σ-Models IN THE D=2 HARMONIC SUPERSPACE

Abstract

The D=2 (4, 0) and (4, 4) harmonic superspace are constructed. Nonlinear supersymmetric σ-models for both real and complex (4, 0) matter multiplets are obtained. Other features are also discussed.

All (4,0): Sigma models with (4,0) off-shell supersymmetry

“…We will discuss a special class of (4, 0) models in (2, 0) superspace and in (4, 0) projective superspace. (4, 0) models have been discussed in (1, 0) superspace, in harmonic superspace and in components in, e.g., [2,4] and [3,5]. In the quantum theory, anomaly cancellation requires modifying the geometry, with H modified by Chern-Simons terms so that dH ∝ tr(F 2 −R 2 ) [1].…”

“…The fields ϕ α are (2, 0) chiral scalar superfields 4) andφᾱ are their complex conjugatesφᾱ = (ϕ α ) * . The fields Λ µ − are (2, 0) fermionic chiral spinor superfieldsD…”

Virasoro algebra from harmonic superspace

“…(2.4) are true constraints. They are put in the action by the help of Lagrange multiplier superfields [3,4].…”

“…Our idea consists of exploiting the conformal structure of the sU(~)/U( 1 ) --s2 sphere used in the harmonization of the (4,O) ordinary superspace [3,4]. This can easily be achieved by replacing the U(1) Lorentz charges of the standard two-dimensional conformal field theory by U(1) Cartan [SU (2) subgroup] charges.…”

“…For example, to the Lorentz tensors az ,x, /2( $-and the current T P 2 correspond respectively to the U(1) Cartan representations: D + + , a , ++, (6' ) and the quantity T4+. These objects, however, have a natural interpretation in the twodimensional (4,O) harmonic superspace with an SU(2) automorphism group [3,4]. They describe respectively the harmonic derivative [5], the infinitely relaxed HoweStelle-Townsend (HST) and Fayet-Sohnius (FS) hypermultiplets [6,7], and finally the new element, namely, the conformal current.…”